Ballistics and projectile weapons have been studied, mathematically and militarily, for hundreds, if not thousands, of years. The well-known ballistic equations of motion provide a mathematical model for the ideal trajectory of a projectile fired by a weapon, whether the projectile is a small-arms round or an artillery shot. These equations can be used to predict the location of a projectile impact or “impact location”.
Characterizing gun systems may require many experimental trials due to the large number of variables that affect performance. Such systems can be analyzed statistically given sufficiently large sample spaces, which would require firing an infeasible number of artillery shots. Each artillery shot may cost thousands of dollars. Artillery shots are intended to destroy their targets, and as such, typically are only fired on remote, isolated test ranges. Transporting large weapon systems, such as artillery pieces, and a large number of projectiles to a remote location where the weapon can be fired may involve prohibitive expenditures of both time and money. Weapon systems are inherently dangerous—while every effort is made to ensure range safety, some risk to test personnel remains.
Analysis of the precision of artillery systems and their associated error budgets is generally performed using a Root Sum of Squares (RSS) approach. RSS uses a variation value, or standard deviation from a prescribed value, that is determined for each component in a system, to estimate a total error, or accumulation, based on taking a square root of the sum of squares of the standard deviations. A sensitivity analysis may also be performed to arrive at a better estimate. In this case each error component has a relative weight associated with it. This analysis typically involves calculating partial derivatives for each error source in the system. This is often difficult or impossible, if the system cannot be described by a closed form expression.